Numerical parameterization implicit surfaces of the form f (x, y, z) = 0

#1 Posted: 2015/5/29 20:25:23

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The grid lines are found by Draghilev Method
Method 1.
Building a line of intersection of the required surface
with the plane x = 0. This line is rotated in steps of 2 * Pi / s
about a vertical axis by an angle 2 * Pi, where s is the number of steps (the grid lines)

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Davide Carpi 2015/5/31 07:19:00

#2 Posted: 2015/5/29 20:39:51

Fridel Selitsky

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Method 2.
The rectangular grid

ELLIPSE3d2.pdf (631.16 KiB) downloaded 722 time(s).

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Davide Carpi 2015/5/31 07:19:00

#3 Posted: 2016/12/17 18:17:47

Fridel Selitsky

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The graph an implicit surface depicted by lines
Examples of the idea of the algorithm taken from the publication of Alexey Ivanov
http://www.mapleprimes.com/questions/219995-Finding-A-Convinient-Parametrization-Of-Surfaces#answer233804

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Вячеслав Мезенцев 2016/12/19 01:43:00, Davide Carpi 2016/12/18 19:04:00, frapuano 2016/12/18 05:42:00

#4 Posted: 2017/1/29 16:56:41

Fridel Selitsky

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Two surfaces are taken from the site
http://xrt.wikidot.com/gallery:implicit
The calculation algorithm:
1.Find the line of intersection of the given surface with the plane Z=0
2.Through each point hold the plane x1 = C and find the line of intersection of that plane with a given surface.These lines represent a given surface.

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Davide Carpi 2017/1/30 09:18:00

#5 Posted: 2017/1/29 23:28:16

Jean Giraud

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Thanks for these two animations. In each one, the last three plots
stay red, though the animated plot works fine. A small detail:
each work sheet has three definitions left over at page 17.

Jean

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Davide Carpi 2017/1/30 09:18:00

#6 Posted: 2017/1/30 03:51:39

Fridel Selitsky

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Thank you Jean,
Worksheets corrected. In addition, in the algorithm for calculating along with x1 = C can be used x2 = C:

double torus x2.sm (73.26 KiB) downloaded 1042 time(s).

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Davide Carpi 2017/1/30 09:18:00, NDTM Amarasekera 2017/1/30 11:30:00

#7 Posted: 2017/1/31 17:50:55

Fridel Selitsky

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The tube in the form of a line of intersection of the cylinder and the torus (See post 7)
http://en.smath.info/forum/yaf_postst2307_Method-A-B--Draghilev-and-animation-spatial-mechanisms.aspx

Time calculation, 9 min.
Villarceau 9.sm (39.38 KiB) downloaded 1016 time(s).

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Davide Carpi 2017/2/1 05:58:00

#8 Posted: 2017/3/1 04:25:37

Fridel Selitsky

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Helical Tube

NonCirc.sm (53.28 KiB) downloaded 1003 time(s).
TubeCir.sm (53.28 KiB) downloaded 1044 time(s).

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Davide Carpi 2017/3/1 06:42:00

#9 Posted: 2017/3/1 04:44:07

Fridel Selitsky

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The surface of the Wikipedia
https://en.wikipedia.org/wiki/File:Tri-brezel.svg

WiciSurf.sm (106.91 KiB) downloaded 1043 time(s).

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Davide Carpi 2017/3/1 06:42:00

#10 Posted: 2017/6/14 13:27:49

Fridel Selitsky

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Non-circular cylindrical vessels with quasi-ellipsoidal ends
Krivoshapko S.N. Ivanov V.N,Encyclopedia of Analytical Surfaces ,Springer,2015

Non-circular cylindrical vessels.pdf (1.26 MiB) downloaded 686 time(s).
Non-circular cylindrical vessels.sm (209.71 KiB) downloaded 1051 time(s).
Shell1.sm (255.15 KiB) downloaded 1077 time(s).
Shell2.sm (33.38 KiB) downloaded 1054 time(s).
Shell3.sm (34.18 KiB) downloaded 1015 time(s).

#11 Posted: 2017/6/15 09:43:57

Jean Giraud

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Thanks Ber7 for the work sheets [Not finished downloading].
If you visit this document, I'm wondering:
"How to add red points in this plot".

Thanks in advance ... Jean

Maths sph2xyz.sm (13.82 KiB) downloaded 1079 time(s).

#12 Posted: 2017/6/15 12:23:51

Fridel Selitsky

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Hello Jean,
Unfortunately, the 3d chart does not allow you to draw points.
Exit (hopefully temporary) -make a 3d chart on a 2d chart.
Maths sph2xyz2d.sm (21.1 KiB) downloaded 1036 time(s).

#13 Posted: 2018/2/6 03:56:52

Fridel Selitsky

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Implicit surfaces in Maxima

ImplicitMaxima.sm (363.82 KiB) downloaded 1073 time(s).

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frapuano 2018/2/6 04:34:00, Martin Kraska 2018/2/6 04:59:00, Radovan Omorjan 2018/2/6 06:22:00

#14 Posted: 2018/2/6 05:06:49

Martin Kraska

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Nice examples!

Just some remarks for those who want to play around with Maxima Draw.

Instead of Image region with Draw() command you can use Maxima Draw3D region with interactive zoom, rotation and resize and a settings dialog.
Insert-> Maxima-> Draw3D
The performance isn't overwhelming, as the image is recalculated for each interaction.
The snippet "draw" provides help texts for the available draw commands and options.
Follow the link in my signature to see how to configure SMath with Maxima.

ImplicitMaxima_Kr.sm (492.51 KiB) downloaded 1097 time(s).

2018-02-06 08_55_49-SMath Studio - [ImplicitMaxima.sm_].png

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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Вячеслав Мезенцев 2018/2/6 06:15:00, Radovan Omorjan 2018/2/6 06:22:00, frapuano 2018/2/6 10:28:00, Fridel Selitsky 2018/2/6 05:08:00

#15 Posted: 2018/2/21 16:41:18

Fridel Selitsky

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Continuation:

MaximPlus1.sm (237.91 KiB) downloaded 1038 time(s).

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frapuano 2018/2/21 18:56:00

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Numerical parameterization implicit surfaces of the form f (x, y, z) = 0 - Messages